To deal with the sickly sweet elephant in the room: no, Candy Crush Saga isn’t included. Not for reasons of snobbery, but rather because surely anyone with an interest in playing puzzle games on their phone will know about it by now.

Candy Crush Saga’s popularity shows the appetite for small-screen puzzling, though, so what else is available on your smartphone or tablet to stretch your brains?

Here are ten of the best games – all available for both Android and iOS with a few also on Windows Phone – to get your grey cells fizzing. The links for each platform lead to the app stores, while “IAP” indicates in-app purchases.

Monument Valley (£2.99 + IAP)iOS / Android / Windows PhoneMonument Valley isn’t the longest mobile game you’ll play, but it’s one of the most beautiful. You guide a princess called Ida through a succession of physics-challenging levels, twisting the scenery to clear her way. With no time limits, the pace is relaxing, but the sense of achievement is huge.

Monument Valley.

Triple Town (Free + IAP)iOS / AndroidOne of the oldest games on this list, but still one of the best puzzlers you can play on a smartphone or tablet. Triple Town involves building a town by matching trees and houses to make bigger versions. It’s wonderfully (if sometimes work and sleep-cripplingly) addictive, with decidedly unaggressive in-app purchases.

Threes! (Free - £2.30)iOS / Android / Windows PhoneThrees! is simple at its core: slide numbered cards into one another to add them up, carrying on for as long as you can before filling the on-screen board. It’s as addictive as Triple Town: you’ll keep wanting one more go, with just enough of a maths element to persuade you you’re not wasting your life. Possibly.

Threes!

The Room Two (£1.99)iOS / AndroidThis is the second game in developer Fireproof Studios’ series – with a third coming soon – and it’s brilliant. This “physical puzzler wrapped in a mystery game” sees you twisting and prodding on-screen items to solve a cryptic tale. The graphics are top-notch, and the puzzles are genuinely challenging.

Framed (£1.79)iOS / AndroidIf there’s a theme in this roundup, it’s the reminder that the puzzle genre is more than just swapping coloured objects on grids. Framed, for example, sees you switching comic-strip panels to progress in the game, with visuals to match. Oh, and a jazzy soundtrack that complements the action perfectly.

Lara Croft Go (£3.99 + IAP)iOS / Android / Windows PhoneThe Tomb Raider games always had a big puzzling element to them. Lara Croft Go makes it the focus: a cleverly-designed turn-based adventure with a range of taxing puzzles to solve. And if you’re not a huge fan of Lara, do try this game’s predecessor Hitman Go, which took a similarly-polished approach to the Hitman franchise.

Spider: Rite of the Shrouded Moon (£3.99)iOS / AndroidThis is the sequel to the just-as-marvellous Spider: The Secret of Bryce Manor. Like that game, you play a spider exploring an empty mansion, solving puzzles including spinning your webs to catch insects. The joy here isn’t just in the puzzles, but in the storyline that reveals itself as you progress: a proper work of craft.

Spider: Rite of the Shrouded Moon.

Dots: A Game About Connecting (Free + IAP)iOS / AndroidThis might have the best claim at being the smartphone gaming era’s Tetris – not a phrase to be used lightly. Dots has you tracing lines (and, if you’re lucky, boxes) through coloured dots to make them disappear, with a beautifully-weighted system of power-ups and a choice of timed, move-limited or endless modes.

Dots.

Best Fiends (Free + IAP)iOS / AndroidThere’s been a rush of games where you match things at the bottom of the screen to kill enemies at the top, from Puzzle Quest to Puzzle & Dragons. Best Fiends is the best of them all, though: from its slug and bug characters to the balance of its gameplay. It also walks the line well between testing your brain and demanding your wallet, unlike some of its peers.

Best Fiends.

Blek (£2.49)iOS / AndroidMore line-tracing and coloured circles here, but Blek is one of the most original mobile puzzlers available. Your job is to connect the circles while avoiding black holes, but the fun here comes in finding your own routes rather than seeking the sole solution to any given level. A minimalist masterpiece.

Blek. Photograph: PR

Weeding down a longlist of great puzzle games to just 10 was a hard task. Triple Town’s follow-up Alphabear was unlucky to miss out, for example: if you love word games, it’s fabulous.

Finally, brand new as this roundup was being written was SPL-T by Simogo, the developer of the wonderful narrative games Year Walk, Device 6 and The Sailor’s Dream. I’m still getting to grips with its box-splitting intricacies, but it looks like a keeper too.

What are your recommendations? The comments section is open for your suggestions.